Ask the person who invited you to share a link to the folder, rather than adding you as a member

Can I receive shared files when I don’t have a Dropbox account?

You don’t need a Dropbox account to view the files in a shared link, and you can download those files to your computer. Files that you download from a shared link won’t sync with Dropbox if you edit them.

Can I upload files to Dropbox without a Dropbox account?

If someone requests files from you, you don’t need a Dropbox account to upload files into the file request. However, without a file request, you need a Dropbox account to upload and share files.